An investigation of the permeability for viscous flow through random fiber structures used as preforms in composite fabrication processes is presented. A method derived from the electrical conduction principles is employed to predict the viscous permeability of the fiber structures directly from their formation factor, specific surface area, and porosity. The recent Brownian diffusion random-walk simulation results on the molecular survival time are used to derive an upper bound and an approximation to the viscous permeability of these structures. The results are compared to experimental data and theoretical models of the literature. It is found that the conduction-based method provides very good permeability estimates in most cases, resulting in an overall ratio of the theoretical prediction to experimental measurement in the proximity of 1 for the over 500 experimental points utilized. This is one of the most comprehensive experimental validations of the conduction-based method to date and its first validation for anisotropic particle beds. A tortuosity analysis indicates a stronger pore-geometry effect on viscous flow relative to any type of diffusional flow, enhancing the understanding of the differences between pressure-driven and diffusion-driven composite manufacturing techniques.

We present a random walk based investigation of the pore size probability distribution and its moments, the survival probability and mean survival time, and the principal relaxation time, for random and ordered arrays of cylindrical fibers of various orientation distributions. The dimensionless mean survival time, principal relaxation time, mean pore size, and mean square pore size are found to increase with porosity, remain practically independent of the directionality of random fiber beds, and attain lower values for ordered arrays. Wide pore size distributions are obtained for random fiber structures and relatively narrow for ordered square arrays, all in very good agreement with theoretically predicted limiting values. Analytical results derived for the pore size probability and its lower moments for square arrays of fibers practically coincide with the corresponding simulation results. Earlier variational bounds on the mean survival time and principal relaxation time are obeyed by our numerical results in all cases, and are found to be quite sharp up to very high porosities. Dimensionless groups representing the deviation of such bounds from our simulation results vary in practically the same range as the corresponding values reported earlier for beds of spherical particles. A universal scaling expression of the literature relating the mean survival time to the mean pore size ͓S. Torquato and C. L. Y. Yeong, J. Chem. Phys. 106, 8814 ͑1997͔͒ agrees very well with our results for all types of fiber structures, thus validated for the first time for anisotropic porous media.

Computer simulation results are presented for the mean survival time, principal relaxation time, mean pore size, and mean square pore size, for random porous structures consisting of parallel nonoverlapping or partially overlapping fibers. The numerical procedure is based on a discrete step-by-step random walk mechanism simulating the Brownian diffusion trajectories of molecules in the porous media. Numerical results on the viscous permeability of these structures are computed with a method based on electrical conduction principles and compared to a variational bound derived from the mean survival time. The results show that nonoverlapping fiber structures exhibit lower values of the dimensionless mean survival time, principal relaxation time, mean pore size, and mean square pore size than randomly overlapping fiber structures of the same porosity, while partially overlapping fiber structures show behavior intermediate to those of the two extreme cases. The mean square pore size (second moment of the pore size distribution) is found to be a very good predictor of the mean survival time for non-, partially, and randomly overlapping fiber structures. Dimensionless groups representing the deviation of variational bounds from our simulation results vary in practically the same range as the corresponding values reported earlier for beds of spherical particles. A universal scaling expression of the literature relating the mean survival time to structural properties [S. Torquato and C. L. Y. Yeong, J. Chem. Phys. 106, 8814 (1997)] agrees very well with our results for all examined fiber structures, thus validated for the first time for porous media formed by partially overlapping particles. The permeability behavior of partially overlapping fiber structures resembles that of nonoverlapping fiber structures for flow parallel to the fibers, but not for transverse flow, where percolation phenomena prevail. The permeability results for beds of unidirectional partially overlapping fibers of moderate and low hard-core porosity compliment successfully earlier numerical data on the permeability of similar structures originating from high-porosity beds of nonoverlapping fibers.